Symmetry correspondence is analogous to stereo and motion correspondence problems. Unlike the other two, symmetry correspondence was completely ignored in prior research. The importance of this problem is related to the fact that 3D symmetry of objects is the most fundamental a priori constraint used by the human visual system in recovering 3D shapes of the objects (Li et al., 2009, 2011). 3D mirror symmetry is easy to verify in 3D representations: pairs of mirror symmetrical points form parallel lines segments that are bisected by the symmetry plane. However, a 2D perspective image of a 3D mirror-symmetrical shape is almost never symmetrical. How is the visual system able to establish 3D symmetry correspondence in 2D asymmetrical images? Similarly to the other two correspondence problems, solving symmetry correspondence in an image is an ill-posed problem because (1) a given edge can have many possible correspondences; (2) any two edges can have infinitely many spurious 3D symmetrical interpretations (Sawada et al., 2011). In this study, we show which a priori constraints have to be used in order to correctly solve the symmetry correspondence problem. The solution begins with solving figure-ground organization (FGO) problem in 3D and 2D representations. This is done based on coarse information provided by a pair of images obtained by a stereoscopic camera. The 3D FGO is used to estimate the plane of symmetry of the 3D object, assuming that this plane is orthogonal to the ground plane, and the 2D vanishing point representing the 3D symmetry in perspective images. We then extract edges within regions of the 2D image representing individual objects (figures). Finally, we detect pairs of symmetric curves by evaluating their (i) relation to the vanishing point, (ii) relative 2D orientation and (ii) relative distance. We will illustrate this model with real images of real objects.
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机译：对称对应类似于立体声和运动对应问题。与其他两个不同，对称对应在先前的研究中被完全忽略。这个问题的重要性与以下事实有关：对象的3D对称性是人类视觉系统在恢复对象的3D形状时使用的最基本的先验约束（Li等，2009，2011）。 3D镜像对称性很容易在3D表示中进行验证：成对的镜像对称点形成平行线段，这些线段被对称平面一分为二。但是，具有3D镜像对称形状的2D透视图图像几乎从不对称。视觉系统如何在2D非对称图像中建立3D对称对应关系？与其他两个对应问题相似，解决图像中的对称对应问题是一个不适当地的问题，因为（1）给定的边缘可能具有许多可能的对应关系; （2）任何两个边缘可以具有无限多个虚假的3D对称解释（Sawada等，2011）。在这项研究中，我们表明必须使用先验约束才能正确解决对称对应问题。解决方案始于解决3D和2D表示形式中的地物组织（FGO）问题。基于由立体摄像机获得的一对图像提供的粗略信息来完成此操作。 3D FGO用于估计3D对象的对称平面，假定该平面与地面正交，并且2D消失点表示透视图像中的3D对称性。然后，我们提取2D图像区域中代表单个对象（图）的边缘。最后，我们通过评估对称曲线对（i）与消失点的关系，（ii）相对2D方向和（ii）相对距离来检测对称曲线对。我们将用真实物体的真实图像说明该模型。
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